Fortelling catastrophes?

A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is generically preceded by a precursor phase which is less rapid, that we characterize. In this model, if an external source of noise exist, the correlation length of the fluctuations increases before the transition, and its spectrum tends to drift towards lower frequencies. This change in the fluctuations could be a way of detecting catastrophic events before they happen.
Comment: This paper contains 7p. and 4 figures. It is also submitted at the Paris Conference intitled "Science du Nonlineaire", 16-18 Mars 2011, and will be published in "Comptes Rendus du Nonmlineaire, Non-lin\'eaire publications Paris France, 03 2011